An office supply company ordered a lot of 400 printers. When the lot arrives the company inspector will randomly inspect 12 printers. If more than three printers in the sample are non-conforming, the lot will be rejected. If fewer than two printers are nonconforming, the lot will be accepted. Otherwise, a second sample of size 8 will be taken. Suppose the inspector finds two non-conforming printers in the first sample and two in the second sample. Also AQL and LTPD are 0.05 and 0.10 respectively. Let incoming quality be 4%.

(i) What is the probability of accepting the lot at the first sample?
(ii) What is the probability of accepting the lot at the second sample? 

An office supply company ordered a lot of 400 printers. When the lot arrives the company inspector will randomly inspect 12 printers. If more than three printers in the sample are non-conforming, the lot will be rejected. If fewer than two printers are nonconforming, the lot will be accepted. Otherwise, a second sample of size 8 will be taken. Suppose the inspector finds two non-conforming printers in the first sample and two in the second sample. Also AQL and LTPD are 0.05 and 0.10 respectively. Let incoming quality be 4%.

(i) What is the probability of accepting the lot at the first sample?
(ii) What is the probability of accepting the lot at the second sample? 

If a researcher wants to find the relationship between today’s unemployment and that of 5 years ago without considering what happens in between then the partial autocorrelation is the better way in comparison to autocorrelation.

At a call centre, callers have to wait till an operator is ready to take their call. To monitor this process, 5 calls were recorded every hour for the 8-hour working day. The data below shows the waiting time in seconds:

(i) Use the data to construct control charts for mean and comments about the
process. If process is out of control, then calculate the revised control limits.
(ii) Construct the CUSUM chart when the process is under control and draw the
conclusion about the process.
(iii) If the specification limits as the 8±2, then calculate the process capability index
Cpk and impetrate the result.
(iv) Also find the percentage of calls lie outside the specification limits assuming
that calls follow the normal distribution. 

The R- chart is suitable when subgroup size is greater than 10.

An office supply company ordered a lot of 400 printers. When the lot arrives the
company inspector will randomly inspect 12 printers. If more than three printers in the
sample are non-conforming, the lot will be rejected. If fewer than two printers are nonconforming, the lot will be accepted. Otherwise, a second sample of size 8 will be
taken. Suppose the inspector finds two non-conforming printers in the first sample and
two in the second sample. Also AQL and LTPD are 0.05 and 0.10 respectively. Let
incoming quality be 4%.
(i) What is the probability of accepting the lot at the first sample?
(ii) What is the probability of accepting the lot at the second sample? 

In single sampling plan, if we increase acceptance number then the OC curve will be steeper.

Differentiate between the autoregressive and moving average models of time series.